mixture systems

Question

Joey had $85 but spent every last bit buying 140 pieces of candy. The yummies cost 75 cents each and the delishes cost 50 cents each. How many pieces of each kind did he buy?

Answer 1

Let y = # Yummies

Let d = # delishes

 

We can set up 2 equations from the information given:

 

1)  y + d = 140      Joey bought 140 pieces of candy

 

The cost will be $.75(y) + $.5d

This will total to $85 giving us:

 

2)  .75y + .5d = 85

 

From equation 1 we can solve for y or d

y+d = 140

y = 140-d

 

Replace y with 140-d in equation 2 and solve for d

 

.75(140-d) + .5d = 85

Distribute the .75 through the parenthesis

.75(140) + .75(-d) + .5d = 85

105 - .75d + .5d = 85

105 - .25d = 85

subtract the 105 from both sides to isolate the variable d

105 - .25d - 105 = 85 - 105

-.25d = -20

Divide both sides by -.25 to isolate a single d

-.25d/-.25 = -20/-.25

d = 80

 

Joey bought 80 delishes

We know the total # candies bought was 140 so

Joey bought 60 yummies

 

Check answer:

.75y + .5d = 85

.75(60) + .5(80) = 85

45 + 40 = 85

85 = 85

Our answer fits the information given.

 

Let me know if you have any questions.

Good luck.  Cheers.

 

Andrew